Abstract

We present a fiber-coupled balanced optical cross-correlator using waveguides in periodically-poled KTiOPO4 (PPKTP). The normalized conversion efficiency of the waveguide device is measured to be η0 = 1.02% / [W·cm2], which agrees well with theory and simulation. This result represents an expected improvement of a factor of 20 over previous bulk-optic devices. The sensitivity of the cross-correlator is characterized and shown to be comparable to the free-space bulk-optic version, with the potential for significant performance enhancements in the future.

© 2014 Optical Society of America

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  1. A. Benedick, J. G. Fujimoto, F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
    [CrossRef]
  2. J. Kim, J. A. Cox, J. Chen, F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
    [CrossRef]
  3. M. Y. Peng, P. T. Callahan, A. H. Nejadmalayeri, S. Valente, M. Xin, L. Grüner-Nielsen, E. M. Monberg, M. Yan, J. M. Fini, F. X. Kärtner, “Long-term stable, sub-femtosecond timing distribution via a 1.2-km polarization-maintaining timing link: approaching 10−21 link stability,” Opt. Express 21(17), 19982–19989 (2013).
    [CrossRef] [PubMed]
  4. J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett. 32(9), 1044–1046 (2007).
    [CrossRef] [PubMed]
  5. A. H. Nejadmalayeri, F. N. C. Wong, T. D. Roberts, P. Battle, F. X. Kärtner, “Guided wave optics in periodically poled KTP: quadratic nonlinearity and prospects for attosecond jitter characterization,” Opt. Lett. 34(16), 2522–2524 (2009).
    [CrossRef] [PubMed]
  6. A. H. Nejadmalayeri, J. A. Cox, J. Kim, F. N. C. Wong, T. D. Roberts, P. Battle, and F. X. Kärtner, “Phase noise measurement of mode locked lasers using guided wave PPKTP balanced cross correlators,” in Conference on Lasers and Electro-Optics 2010, OSA Technical Digest (Optical Society of America, 2010), paper JTuD75.
    [CrossRef]
  7. R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
    [CrossRef]
  8. P. T. Callahan, T. D. Roberts, P. Battle, A. H. Nejadmalayeri, and F. X. Kärtner, “A hybrid integrated balanced optical cross-correlator using PPKTP waveguides,” in Conference on Lasers and Electro-Optics 2013, OSA Technical Digest (Optical Society of America, 2013), paper CW3B.6.
    [CrossRef]
  9. L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
    [CrossRef]
  10. T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28(11), 947–949 (2003).
    [CrossRef] [PubMed]
  11. T. Suhara and M. Fujimura, Waveguide Nonlinear-Optic Devices, (Springer, 2003). Chap. 3.
  12. A. B. Fallahkhair, K. S. Li, T. E. Murphy, “Vector Finite Difference Modesolver for Anisotropic Dielectric Waveguides,” J. Lightwave Technol. 26(11), 1423–1431 (2008).
    [CrossRef]
  13. M. G. Roelofs, A. Suna, W. Bindloss, J. D. Bierlein, “Characterization of optical waveguides in KTiOPO4 by second-harmonic spectroscopy,” J. Appl. Phys. 76(9), 4999–5006 (1994).
    [CrossRef]
  14. F. König, F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch,” Appl. Phys. Lett. 84(10), 1644–1646 (2004).
    [CrossRef]
  15. K. Fradkin, A. Arie, A. Skliar, G. Rosenman, “Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO4,” Appl. Phys. Lett. 74(7), 914–916 (1999).
    [CrossRef]
  16. K. Kato, E. Takaoka, “Sellmeier and thermo-optic dispersion formulas for KTP,” Appl. Opt. 41(24), 5040–5044 (2002).
    [CrossRef] [PubMed]
  17. H. Vanherzeele, J. D. Bierlein, “Magnitude of the nonlinear-optic coefficients of KTiOPO4,” Opt. Lett. 17(14), 982–984 (1992).
    [CrossRef] [PubMed]

2013 (2)

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[CrossRef]

M. Y. Peng, P. T. Callahan, A. H. Nejadmalayeri, S. Valente, M. Xin, L. Grüner-Nielsen, E. M. Monberg, M. Yan, J. M. Fini, F. X. Kärtner, “Long-term stable, sub-femtosecond timing distribution via a 1.2-km polarization-maintaining timing link: approaching 10−21 link stability,” Opt. Express 21(17), 19982–19989 (2013).
[CrossRef] [PubMed]

2012 (1)

A. Benedick, J. G. Fujimoto, F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
[CrossRef]

2009 (1)

2008 (2)

A. B. Fallahkhair, K. S. Li, T. E. Murphy, “Vector Finite Difference Modesolver for Anisotropic Dielectric Waveguides,” J. Lightwave Technol. 26(11), 1423–1431 (2008).
[CrossRef]

J. Kim, J. A. Cox, J. Chen, F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
[CrossRef]

2007 (1)

2004 (1)

F. König, F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch,” Appl. Phys. Lett. 84(10), 1644–1646 (2004).
[CrossRef]

2003 (1)

2002 (2)

K. Kato, E. Takaoka, “Sellmeier and thermo-optic dispersion formulas for KTP,” Appl. Opt. 41(24), 5040–5044 (2002).
[CrossRef] [PubMed]

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

1999 (1)

K. Fradkin, A. Arie, A. Skliar, G. Rosenman, “Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO4,” Appl. Phys. Lett. 74(7), 914–916 (1999).
[CrossRef]

1994 (1)

M. G. Roelofs, A. Suna, W. Bindloss, J. D. Bierlein, “Characterization of optical waveguides in KTiOPO4 by second-harmonic spectroscopy,” J. Appl. Phys. 76(9), 4999–5006 (1994).
[CrossRef]

1992 (1)

Arie, A.

K. Fradkin, A. Arie, A. Skliar, G. Rosenman, “Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO4,” Appl. Phys. Lett. 74(7), 914–916 (1999).
[CrossRef]

Battle, P.

Benedick, A.

A. Benedick, J. G. Fujimoto, F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
[CrossRef]

Bierlein, J. D.

M. G. Roelofs, A. Suna, W. Bindloss, J. D. Bierlein, “Characterization of optical waveguides in KTiOPO4 by second-harmonic spectroscopy,” J. Appl. Phys. 76(9), 4999–5006 (1994).
[CrossRef]

H. Vanherzeele, J. D. Bierlein, “Magnitude of the nonlinear-optic coefficients of KTiOPO4,” Opt. Lett. 17(14), 982–984 (1992).
[CrossRef] [PubMed]

Bindloss, W.

M. G. Roelofs, A. Suna, W. Bindloss, J. D. Bierlein, “Characterization of optical waveguides in KTiOPO4 by second-harmonic spectroscopy,” J. Appl. Phys. 76(9), 4999–5006 (1994).
[CrossRef]

Callahan, P. T.

Chen, J.

J. Kim, J. A. Cox, J. Chen, F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
[CrossRef]

J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett. 32(9), 1044–1046 (2007).
[CrossRef] [PubMed]

Cox, J. A.

J. Kim, J. A. Cox, J. Chen, F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
[CrossRef]

Fallahkhair, A. B.

Fini, J. M.

Fradkin, K.

K. Fradkin, A. Arie, A. Skliar, G. Rosenman, “Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO4,” Appl. Phys. Lett. 74(7), 914–916 (1999).
[CrossRef]

Fujimoto, J. G.

Gopinath, J. T.

Grein, M. E.

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

Grüner-Nielsen, L.

Haderka, O.

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[CrossRef]

Haus, H. A.

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

Ippen, E. P.

Jiang, L. A.

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

Kaertner, F. X.

Kärtner, F. X.

Kato, K.

Kim, J.

Kolodziejski, L. A.

König, F.

F. König, F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch,” Appl. Phys. Lett. 84(10), 1644–1646 (2004).
[CrossRef]

Kuzucu, O.

Li, K. S.

Loehl, F.

Machulka, R.

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[CrossRef]

Monberg, E. M.

Murphy, T. E.

Nejadmalayeri, A. H.

Peng, M. Y.

Perina, J.

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[CrossRef]

Petrich, G. S.

Roberts, T. D.

Roelofs, M. G.

M. G. Roelofs, A. Suna, W. Bindloss, J. D. Bierlein, “Characterization of optical waveguides in KTiOPO4 by second-harmonic spectroscopy,” J. Appl. Phys. 76(9), 4999–5006 (1994).
[CrossRef]

Rosenman, G.

K. Fradkin, A. Arie, A. Skliar, G. Rosenman, “Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO4,” Appl. Phys. Lett. 74(7), 914–916 (1999).
[CrossRef]

Schibli, T. R.

Schlarb, H.

Skliar, A.

K. Fradkin, A. Arie, A. Skliar, G. Rosenman, “Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO4,” Appl. Phys. Lett. 74(7), 914–916 (1999).
[CrossRef]

Soubusta, J.

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[CrossRef]

Suna, A.

M. G. Roelofs, A. Suna, W. Bindloss, J. D. Bierlein, “Characterization of optical waveguides in KTiOPO4 by second-harmonic spectroscopy,” J. Appl. Phys. 76(9), 4999–5006 (1994).
[CrossRef]

Svozilík, J.

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[CrossRef]

Takaoka, E.

Tandon, S. N.

Valente, S.

Vanherzeele, H.

Wong, F. N. C.

Wong, S. T.

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

Xin, M.

Yan, M.

Zhang, Z.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

F. König, F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch,” Appl. Phys. Lett. 84(10), 1644–1646 (2004).
[CrossRef]

K. Fradkin, A. Arie, A. Skliar, G. Rosenman, “Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO4,” Appl. Phys. Lett. 74(7), 914–916 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[CrossRef]

J. Appl. Phys. (1)

M. G. Roelofs, A. Suna, W. Bindloss, J. D. Bierlein, “Characterization of optical waveguides in KTiOPO4 by second-harmonic spectroscopy,” J. Appl. Phys. 76(9), 4999–5006 (1994).
[CrossRef]

J. Lightwave Technol. (1)

Nat. Photonics (2)

A. Benedick, J. G. Fujimoto, F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
[CrossRef]

J. Kim, J. A. Cox, J. Chen, F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

R. Machulka, J. Svozilík, J. Soubusta, J. Peřina, O. Haderka, “Spatial and spectral properties of fields generated by pulsed second-harmonic generation in a periodically poled potassium-titanyl-phosphate waveguide,” Phys. Rev. A 87(1), 013836 (2013).
[CrossRef]

Other (3)

P. T. Callahan, T. D. Roberts, P. Battle, A. H. Nejadmalayeri, and F. X. Kärtner, “A hybrid integrated balanced optical cross-correlator using PPKTP waveguides,” in Conference on Lasers and Electro-Optics 2013, OSA Technical Digest (Optical Society of America, 2013), paper CW3B.6.
[CrossRef]

A. H. Nejadmalayeri, J. A. Cox, J. Kim, F. N. C. Wong, T. D. Roberts, P. Battle, and F. X. Kärtner, “Phase noise measurement of mode locked lasers using guided wave PPKTP balanced cross correlators,” in Conference on Lasers and Electro-Optics 2010, OSA Technical Digest (Optical Society of America, 2010), paper JTuD75.
[CrossRef]

T. Suhara and M. Fujimura, Waveguide Nonlinear-Optic Devices, (Springer, 2003). Chap. 3.

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Figures (6)

Fig. 1
Fig. 1

An illustration of the principle of balanced optical cross-correlation. Pulses at the fundamental (represented in green) propagate through the nonlinear crystal (represented in blue) at different speeds, generating different amounts of SH light (represented as orange pulses) on the forward and reverse paths. The difference in detected SH power then gives the output voltage error curve, in which the voltage is proportional to the time separation of the pulses. Abbreviations are as follows: DM – dichroic mirror, PD – photodetector, WDM – wavelength division multiplexer.

Fig. 2
Fig. 2

Calculated electric field distributions in the waveguide for the TE and TM modes at the fundamental frequency and the TE mode at the second harmonic. The refractive index profile for ny is illustrated at bottom right. Here again we refer to the y-polarized mode as the TE mode. Mode profiles were calculated using MATLAB and are normalized for unity power.

Fig. 3
Fig. 3

(a) Photograph of a packaged fiber-coupled BOC module. (b) Diagram of experimental setup for measuring conversion efficiency. Abbreviations are as follows: CW – continuous-wave laser, EDFA – erbium-doped fiber amplifier, PC – polarization controller, PD – photodetector.

Fig. 4
Fig. 4

(a) Second harmonic power generated in the waveguide as a function of input power (after coupling calibration). Quadratic fit to the data shown as solid black line. (b) Second harmonic power as a function of input wavelength.

Fig. 5
Fig. 5

(a) Diagram of experimental setup for measuring cross-correlation traces with the fiber-coupled BOCs. Abbreviations are as follows: MLL – mode-locked laser, HWP – half-wave plate, QWP – quarter-wave plate, PBS – polarization beam-splitter, COLL – collimator, WDM – wavelength-division multiplexer, BPD – balanced photodetector, CTRL – controller. (b) Typical balanced cross-correlation trace from fiber-coupled BOC. Detector output voltage recorded as a function of the time delay between the two FH input pulses.

Fig. 6
Fig. 6

Fiber-coupled BOC sensitivity as a function of (a) temperature and (b) total average FH power at the input of the WDM. Red squares and blue diamonds denote the two fiber-coupled modules, green triangles denote a typical bulk-optic BOC for comparison. Sensitivity was determined by a linear regression fit to the linear region at the zero-crossing of the cross-correlation curve. Error bars in (a) denote the confidence interval of the fit.

Equations (22)

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E t ( x,y,z )= m Am( x ) E tm( y,z ) e j β m x
H t ( x,y,z )= m Am( x ) H tm( y,z ) e j β m x
1 2 Re{ E tm × H tn * } dydz= δ mn
d A 1 / dx =j κ 1 A 3 ( x ) A 2 * ( x ) e j2Δx
d A 2 / dx =j κ 2 A 3 ( x ) A 1 * ( x ) e j2Δx
d A 3 / dx =j κ 3 A 1 ( x ) A 2 ( x ) e +j2Δx
κ 1 = κ 2 =( ω ε 0 d eff /2 ) E 1 * E 2 * E 3 dydz
κ 3 =( ω ε 0 d eff ) E 1 E 2 E 3 * dydz
A 3 ( L )=j κ 3 A 10 A 20 L e +jΔL sinc( ΔL )
P SH = η 0 L 2 P FH 2 | A 3 ( L ) | 2 = η 0 L 2 ( | A 10 | 2 + | A 20 | 2 ) 2 =4 η 0 L 2 A 0 4
η 0 = κ 3 2 sin c 2 ( ΔL ) /4
A 1 ( x,t )= A 10 e ( t ζ 1 x ΔT /2 ) 2 / τ 2
A 2 ( x,t )= A 20 e ( t ζ 2 x+ ΔT /2 ) 2 / τ 2
ζ i =( v gi 1 v g3 1 )
A 3 ( L,t )= j π κ 3 A 10 A 20 2c e ( at+ bΔT 2 ) 2 [ erf( cL+ aΔT 2 bt )erf( aΔT 2 bt ) ]
a 2 = ( ζ 1 ζ 2 ) 2 τ 2 ( ζ 1 2 + ζ 2 2 ) , b 2 = ( ζ 1 + ζ 2 ) 2 τ 2 ( ζ 1 2 + ζ 2 2 ) , c 2 = ( ζ 1 2 + ζ 2 2 ) τ 2
A 3 ( L,t )= j π κ 3 A 10 A 20 τ 8 ζ e 2 t 2 / τ 2 [ erf( 2ζL+ΔT 2 τ )erf( ΔT 2 τ ) ]
J=α f rep | A 3 ( L,t ) | 2 dt
ΔV( ΔT' )= Gα f rep κ 3 2 A 10 2 A 20 2 ( π τ ) 3 16 ζ 2 [ [ erf( 2ζL+ΔT' 2 τ )erf( ΔT' 2 τ ) ] 2 [ erf( ΔT' 2 τ )erf( ΔT'2ζL 2 τ ) ] 2 ]
K= Gα κ 3 2 P avg,FH 2 4 2 f rep ζ 2 erf( 2ζL 2 τ )[ e ( 2ζL / 2 τ ) 2 1 ]
Δ n i ( λ )= A i + B i λ+ C i λ 2 + F i e ( λ350 / G i ) ,
n i ( λ,y,z )= n 0,i ( λ )+Δ n i ( λ )rect( y/w )erfc( z/h )

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